文章基本信息

标题：Sound Lemma Generation for Proving Inductive Validity of Equations
本地全文：下载
作者：Takahito Aoto
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2008
卷号：2
页码：13-24
DOI：10.4230/LIPIcs.FSTTCS.2008.1737
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In many automated methods for proving inductive theorems, finding a suitable generalization of a conjecture is a key for the success of proof attempts. On the other hand, an obtained generalized conjecture may not be a theorem, and in this case hopeless proof attempts for the incorrect conjecture are made, which is against the success and efficiency of theorem proving. Urso and Kounalis (2004) proposed a generalization method for proving inductive validity of equations, called sound generalization, that avoids such an over-generalization. Their method guarantees that if the original conjecture is an inductive theorem then so is the obtained generalization. In this paper, we revise and extend their method. We restore a condition on one of the characteristic argument positions imposed in their previous paper and show that otherwise there exists a counterexample to their main theorem. We also relax a condition imposed in their framework and add some flexibilities to some of other characteristic argument positions so as to enlarge the scope of the technique.
关键词：Sound generalization; inductive theorem; automated theorem proving; term rewriting